Techniques for sampling an analog signal, converting the sampled signal to digital and processing that signal using digital techniques are known in the art. An example of an analog signal source is that provided by a measurement sensor, such as a thermocouple. The sampled analog signal is converted to digital. Conversion to digital may produce a digital stream of one or more bits. Typically, the analog signal is sampled at one rate, the sampling frequency (fS), while the digital output is needed at a different rate, the output word rate (OWR).
Filters for doing such processing, such as finite impulse response (FIR) filters and FIR Sinc filters, are known. Digital filters such as Sinc filters can be implemented using digital circuits for performing a variety of mathematical operations. Some FIR filters use tables of coefficients for multiplying digital values and performing additions. Multipliers are known which use 2's complement addition to perform multiplication. However, such multipliers require a fair amount of power, machine cycles and silicon real estate to implement.
Certain cascaded integrator comb (CIC) filters described in an article by Eugene B. Hogenauer, entitled “AN ECONOMICAL CLASS OF DIGITAL FILTERS FOR DECIMATION AND INTERPOLATION,” published in IEEE Transactions on Acoustics, Speech and Signal Processing, Volume ASSP-29, No. 2, Apr. 1981, incorporated herein in its entirety by reference (Hogenauer filter), perform the filtering without coefficient multiplication. N integrators, N combs and a subsampling switch comprise an Nth order Hogenauer Sinc filter denoted by SincN The N integrators operate at a high sampling rate, fS, and the N combs operate at a low sampling rate (the subsampling rate) fSS.
The frequency response of a Hogenauer filter depends on the order N of the Sinc filter, a differential delay M, and the integer rate change factor R. The Hogenauer filters produce a frequency response characterized by an equation or a polynomial expression of the equation with roots (also called “zeros”) where attenuation of signals is very strong. R, M, and N are chosen to provide acceptable passband characteristics over the frequency range from zero to a predetermined cutoff frequency, fC, expressed relative to the low sampling rate fSS.
The Hogenauer article, cited above, notes some problems encountered with these filters. One disadvantage is that the frequency response is fully determined by only three integer parameters, resulting in a limited range of filter characteristics. For example, the Hogenauer filter of order N always superimposes all zeros at a frequency f0 (and integral multiples of f0) where f0 is defined as:       f    0    =            1      M        ·          f      ss      This wastes the potential to strongly attenuate other frequencies in the vicinity of the frequency f0.
What is needed are techniques that enable greater freedom in the placement of zeros than allowed by Hogenauer filters, and techniques to tailor the passband characteristics as described without employing the multipliers and large number of registers that greatly increase the use of silicon real estate in other digital filters.